See our review of the first edition. According to the authors' preface, for the new edition several sections have been expanded and clarified and many new problems added. Also new are an appendix giving an alternative approach to differential forms and new sections on Perron's method for solving the Dirichlet problem, Green's functions, an alternative proof of the Riemann mapping theorem, and more. There is also a new historical note by Ranjan Roy.
Preface to Second Edition.- Preface to First Edition.- Standard Notation and Commonly Used Symbols.- 1 The Fundamental Theorem in Complex Function Theory.- 2 Foundations.- 3 Power Series.- 4 The Cauchy Theory - A Fundamental Theorem.- 5 The Cauchy Theory - Key Consequences.- 6 Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions.- 7 Sequences and Series of Holomorphic Functions.- 8 Conformal Equivalence and Hyperbolic Geometry.- 9 Harmonic Functions.- 10 Zeros of Holomorphic Functions.- Bibliographical Notes.- Bibliography.- Index.